Mathematics
Irrational numbers and real numbers
अपरिमेय संख्याएँ और वास्तविक संख्याएँ
In this Class 10 Mathematics topic, students build a clear understanding of real numbers as the collection of rational and irrational numbers. They learn to identify irrational numbers, compare and represent real numbers on the number line, and interpret terminating, recurring, and non-terminating non-recurring decimals. The topic also develops confidence with properties and operations involving real numbers, providing useful foundations for reading polynomial expressions, coefficients, and real zeros in the surrounding Polynomials chapter.
Practice questions
Which of the following options contains only real numbers?EasyLevel 25What type of number is (-\sqrt{7})?EasyLevel 25What type of number is 3√5?EasyLevel 25Which statement is correct about (\frac{\sqrt{2}}{2})?EasyLevel 25What is the sum of two irrational numbers always?EasyLevel 25What is the product of two irrational numbers always?EasyLevel 25What type of number is \(0.\overline{7}\)?EasyLevel 25Which of the following numbers is both a natural number and a rational number?EasyLevel 25What is the correct relation between √2 and √8?EasyLevel 25If (x=\sqrt{3}), what type of number is (x^2)?EasyLevel 25Which number cannot be written in the form (\frac{p}{q}) where (p) and (q) are integers and (q\neq0)?EasyLevel 25Which of the following is a terminating decimal?EasyLevel 25What is the simplest form of \(\sqrt{20}+\sqrt{45}\)?EasyLevel 25Which option can be represented on the number line?EasyLevel 25What is the simplified form of \(\sqrt{27}\)?EasyLevel 25If the decimal expansion of a number is non-terminating but repeating, what type of number is it?EasyLevel 25What is the simplified form of \(\sqrt{2}+\sqrt{8}\)?EasyLevel 25What is the decimal expansion of (\frac{1}{7}) like?EasyLevel 25Which of the following represents the sum of a rational number and an irrational number?EasyLevel 25Which option is always true?EasyLevel 25